Here we give a short review of the basic structure of a noncommutative gauge field theory based on the Seiberg-Witten (SW) construction, first presented in the context of String Theory [1]}. An NC field theory is a field theory defined on a noncommutative space-time, i.e., a space-time described by mutually non-commuting coordinates, \([x^{\mu },x^{\nu }]\ne 0\) . One way to implement this NC structure is to deform the algebra of functions (fields) on ordinary (commutative) space-time, by introducing an NC star-product, the simplest of which is the Moyal-Weyl star-product,
\(f(x)\star g(y)=e^{\frac{i}{2}\theta ^{\mu \nu }\frac{\partial }{\partial x^{\mu }}\frac{\partial }{\partial y^{\nu }}}f(x)g(y)\vert _{y\rightarrow x}.\) 
